- #1
chart2006
- 12
- 0
Homework Statement
The two-dimensional motion of a particle is defined by the relationship [tex] r = \frac {1}{sin\theta - cos\theta} [/tex] and [tex] tan\theta = 1 + \frac {1}{t^2} [/tex], where [tex] r [/tex] and [tex] \theta [/tex] are expressed in meters and radians, respectively, and [tex] t [/tex] is expressed in seconds. Determine (a) the magnitudes of velocity and acceleration at any instant, (b) the radius of curvature of the path.
Homework Equations
[tex] r = \frac {1}{sin\theta - cos\theta} [/tex]
[tex] tan\theta = 1 + \frac {1}{t^2} [/tex]
The Attempt at a Solution
I've made a few attempts but they seem way more complicated than the problem should be I think. I'm assuming I need to solve [tex] tan\theta [/tex] for [tex] \theta [/tex]. Once I've done that I figure I'd need to differentiate both [tex] r [/tex] and [tex] \theta [/tex] to find [tex] \dot{r}, \ddot{r}, \dot{\theta}, \ddot{\theta}[/tex].
I don't know if I'm on the correct route but any help would be appreciated. thanks!